Method and apparatus for code phase tracking

ABSTRACT

A method of code phase tracking for CDMA type communication is disclosed together with apparatus including a GPS receiver ( 10  to  15 ) for the same. The method uses a modified early-minus-late correlation function to determine the code phase error between a target pseudorandom noise code of an incoming signal and locally generated replica codes. The early-minus-late correlation function is modified compared to the true function whereby the gradient of the modified function at zero code phase error is increased. This may be achieved my modifying the early-minus-late correlation function after its derivation. Alternatively, it may be modified by modifying variables from which it is derived and in particular, by modifying the either or both of the power spectrums of the subject signal or the early and late replica code signals whereby at least one odd harmonic is reduced in size or removed; at least one even harmonic is increased in size: or the bandwidth is truncating between harmonics so as to excise an adjacent even harmonic.

[0001] This invention relates to a method of code phase tracking forcode division multiple access (CDMA) type communication and to apparatusfor the same.

[0002] The invention is of particular benefit to the field of globalpositioning systems (GPS) and is described with reference to GPShereafter. However, such reference should not be interpreted as limitingthe scope of the invention to merely OPS For example, the invention isequally applicable to CDMA communication between mobile cellulartelephones and associated networks.

[0003] At present, GPS is most notably associated with the NavigationSystem with Time and Ranging (NAVSTAR) GPS, an all weather, spaced basednavigation system developed and operated by the US Department ofDefense, however, the general principles underlying GPS are universaland not merely limited to NAVSTAR. Accordingly, GPS hereafter refers toany global positioning system comprising a plurality of CDMA radiotransmitters at different locations and a receiver which determines itslocation based on the time of arrival of the transmissions of the radiotransmitters.

[0004] As is well known, a GPS receiver may implement a pseudorandomnoise (PRN) code correlation loop in which early (E), prompt (P) andlate (L) replica codes of satellite PRN codes are continuouslygenerated, and compared to the incoming satellite PRN codes as receivedby the receiver. Using a code phase discriminator calculated as afunction of the correlation, it is then possible to determine whether atarget incoming code has been acquired; if the code phase discriminatorexceeds a predetermined threshold level, the target incoming code andthe locally generated replica codes can be assumed to be in phase, i.e.the code is acquired. If not, the code generator produces the nextseries of replicas with a phase shift, typically of one chip, and thecode phase discriminator is recalculated. Assuming carrier phase lock, alinear code sweep should eventually result in the target incoming codebeing in phase with that of the locally generated replica codes andtherefore, if detected, code acquisition.

[0005] Once the code is acquired, a code phase lock loop may be used totrack the code, typically employing an early-minus-late code correlationfunction in order to determine the code phase error between the targetincoming code and the locally generated replica codes. As code phaseshift is the basis for pseudorange measurements, the accuracy to whichthe pseudoranges can be measured and ultimately to which the position ofthe GPS receiver can be estimated depends on the accuracy to which thecode phase lock loop can determine the code phase error.

[0006] It is therefore an object of the invention to provide a methodand apparatus for code phase tracking able to more accurately determinethe code phase error between a target pseudorandom noise code of anincoming signal and locally generated replica codes.

[0007] According to the present invention, a method of code phasetracking is provided together with a receiver comprising an antenna anda signal processor for the same. The method comprises the steps of:

[0008] (a) receiving a subject signal containing a target pseudorandomnoise code;

[0009] (b) generating a series of signals containing early and latereplica codes corresponding to the target code;

[0010] (c) correlating the subject signal with the early and latereplica code signals and returning respective early and late correlationvalues; and

[0011] (d) determining the code phase error between the target code andthe replica codes from a modified early-minus-late correlation functionderived from the early and late correlation values, the modifiedearly-minus-late correlation function being such that its gradient atzero code phase error is increased compared to the true early-minus-latecorrelation function.

[0012] Increasing the gradient of the early-minus-late correlationfunction at the zero code phase error enables the occurrence of zerocode phase error to be determined more accurately.

[0013] The early-minus-late correlation function may be modified afterits derivation or, alternatively, prior to its derivation by modifyingeither the subject signal, the early and late replica code signals orthe early and late correlation values.

[0014] Modifying any one of the parameters from which theearly-minus-late correlation function is derived may enable thenecessary signal processing to be simplified. For example, modificationof the subject signal may be achieved using relatively simple front-endanalogue circuitry and modification of the early and late replica codesignals may be achieved either by processing unmodified replica signals,say by filtering, or by direct generation of the appropriate sequence,especially if done in the digital domain.

[0015] Modification of the subject signal and/or the early and latereplica code signals preferably including modification of theirrespective power spectrums by at least one of the following: reducing insize or removing at least one odd harmonic; increasing in size at leastone even harmonic; and truncating the bandwidth between harmonics so asto excise an adjacent even harmonic.

[0016] There is believed there is a direct relationship between thepower spectrums of the subject signal/replica signals and theearly-minus-late correlation function such that the aforementionedharmonic manipulation increases the gradient of the early-minus-latecorrelation function at the point of zero code phase error. Thisrelationship together with its effect on the accuracy to which theoccurrence of zero code phase error can be determined is explainedbelow.

[0017] The invention further provides a receiver comprising a signalprocessor for modifying the power spectrum of a received subject signalcontaining a target pseudorandom noise code whereby the power spectrumof the subject signal has either at least one odd harmonic which isreduced in size or removed; at least one even harmonic which isincreased in size; or a reduced bandwidth which is truncated betweenharmonics so as to excise an adjacent even harmonic.

[0018] The invention yet further provides a receiver comprising anantenna for receiving a subject signal containing a target pseudorandomnoise code; and a signal processor comprising a generator for generatinga series of signals containing early and late replica codescorresponding to the target code, a correlator for correlating thesubject signal with the early and late replica code signals andreturning respective early and late correlation values, and means fordetermining the code phase error between the target code and the replicacodes from a modified early-minus-late correlation function derived fromthe early and late correlation values, such that the gradient of themodified early-minus-late correlation function at zero code phase erroris increased compared to the true early-minus-late correlation function.

[0019] The above receiver may modify the early-minus-late correlationfunction by modifying either the subject signal, the early and latereplica code signals or the early and late correlation values prior toderiving the early-minus-late correlation function. In particular, butnot exclusively, the receiver may modify the early-minus-latecorrelation function by modifying the subject signal or the early andlate replica code signals whereby either or both of their respectivepower spectrums have either at least one odd harmonic which is reducedin size or removed; at least one even harmonic which is increased insize; or a reduced bandwidth which is truncated between harmonics so asto excise an adjacent even harmonic.

[0020] The above and other features and advantages of the presentinvention will be apparent from the following description, by way ofexample, of an embodiment of a method of code phase tracking and a GPSreceiver according to the present invention with reference to theaccompanying drawings in which:

[0021]FIG. 1 shows, schematically, an SPS GPS receiver according to thepresent invention:

[0022]FIG. 2 shows, schematically, the receiver channels and receiverprocessor of the GPS receiver of FIG. 1 in greater detail;

[0023]FIG. 3 is a graph showing an idealised early-minus-latecorrelation function for 1.0 MHz and 4.0 MHz bandwidths;

[0024]FIG. 4 is a graph showing the gradient of the early-minus-latecorrelation function plotted against the bandwidth of the incomingsignal for both unmodified and modified incoming signals; and

[0025]FIGS. 5A and 5B are graphs showing normalised power spectrums forboth an unmodified and a modified incoming signal respectively.

[0026] The general principles underlying GPS and methods and apparatusfor its implementation are known. For example, see GPS Principles andApplications (Editor, Kaplan) ISBN 0-89006-793-7 Artech House,hereinafter “Kaplan”.

[0027] As is well known, each NAVSTAR GPS satellite transmits twocarrier frequencies; L1, the primary frequency at 1575.42 MHz and L2,the secondary frequency at 1227.60 MHz. The carrier frequencies aremodulated by spread spectrum codes with a PRN sequence unique to eachsatellite and also by the navigation data message. The L1 signal ismodulated the coarse/acquisition (C/A) code and the precision (P[Y])code whereas the L2 signal is modulated by the P[Y] code only. The P[Y]codes relate to the precise positioning service (PPS) primarily formilitary and select government agency users whereas the C/A relates tothe standard positioning service (SPS) for which there is currentlyunrestricted access.

[0028]FIG. 1 shows, schematically, the architecture of an SPS GPSreceiver according to the present invention. GPS radio frequency (RF)signals are received by an antenna 10 and pre-processed in apre-processor 11 by preamplification, passive bandpass filtering inorder to minimise out-of-band RF interference, further filtering tofilter out first harmonics of the power spectrum of the incoming signal;down converting to an intermediate frequency (IF) and analog to digitalconversion. Digitised IF signals are then provided to each of n digitalreceiver channels 12 in which they are acquired and tracked inco-operation with the receiver processor 13 for the purpose of acquiringnavigation information. Such methods for acquisition and tracking arewell known, for example, see chapter 4 (GPS satellite signalcharacteristics) & chapter 5 (GPS satellite signal acquisition andtracking), Kaplan ibid. Using acquired navigation information and thetime of arrival of the transmissions, the navigation processor 14calculates the position of the receiver using conventional algorithmsand that position is displayed on a display 15 to the user.

[0029] The pre-processor 11 will be typically implemented in the form offront end analogue circuitry with the digital receiver channels 12, thereceiver processor 13 and the navigation processor 14 implemented in theform of a general purpose microprocessor or a microprocessor embedded ina GPS application specific integrated circuit (AIC).

[0030]FIG. 2 shows, schematically, the receiver channel co-operatingwith the receiver processor in greater detail. In order to retrieve theinformation on the incoming signal, a carrier wave (CW) must be removedand this is done by the receiver generating in-phase (I) and quadraturephase (Q) replica carrier wave signals using a carrier wave generator21. The replica carrier waves ideally have the same frequency as thereceived signal, however, due to Doppler shift caused by the relativemovement between the receiver and orbiting satellite, the frequency ofthe GPS signals as received in the receiver normally differs from theprecise satellite transmission frequency. In order to accuratelyreplicate the frequency of the received carrier wave, a conventionalcarrier wave phase lock loop is employed. Although perhaps undesirable,it is possible to omit the carrier phase lock stage altogether as theDoppler shift of the carrier and its associated effect on the code phasediscriminator is reasonably small.

[0031] In order to acquire code phase lock, early (E), prompt (P) andlate (L) replica codes of the PRN sequences are continuously generatedby a code generator 22 at a frequency related to the received carrier(i.e. nominal plus Doppler). The replica codes are then correlated withthe I and Q signals to produce three in-phase correlation components(IE, IL, IP) and three quadrature phase correlation components (QE, QL,QP), typically by integration in an integrator 23 over substantially thewhole of the PRN code. In the receiver processor 13, a code phasediscriminator is calculated as a function of the correlation componentson which a threshold test is applied and a phase match declared if thecode phase discriminator is high. If not, the code generator producesthe next series of replicas with single chip phase advance and the codephase discriminator is recalculated. Any declared phase match isvalidated by recalculating the discriminator, A linear phase sweep willeventually result in the incoming PRN code being in phase with that ofthe locally generated replica and thus code acquisition.

[0032] Once the code is acquired, a code phase lock loop employing anearly-minus-late correlation function is used to track the code. Theearly-minus-late correlation function is modified compared to the trueearly-minus-late correlation function because of the aforementionedfiltering out of the first harmonics of the power spectrum of theincoming signal. As a consequence, the code phase lock loop provides anenhanced code phase error signal relating to the time difference betweenthe incoming signal and the two local generated replicas.

[0033] Without wishing to be bound by any theory, the inventor believesthe following analysis explains the relationship between the accuracy towhich the code phase lock loop can determine the code phase error, thegradient of the early-minus-late correlation function at zero code phaseerror and the aforementioned power spectrum manipulation.

[0034] As previously stated, the accuracy to which the pseudoranges canbe measured and ultimately to which the position of the GPS receiver canbe estimated The relationship between the code phase error measurement(Δt) and an associated pseudorange error measurement (ΔD) can beexpressed as:

Δd≈c Δt  [Equation 1]

[0035] where C is the speed of light. Thus, if the accuracy of thepseudorange measurement is to be determined to 1 meter, the code looperror (after averaging for noise) must be to within 3.3 ns, or about{fraction (1/300)} T_(c) where T_(c) is the GPS L1 C/A signal chipperiod.

[0036] Curves 31 and 32 of FIG. 3 shows the true, normalised,early-minus-late (E−L) correlation function for signal bandwidths of 1.0MHz and 4.0 MHz respectively where the E−L correlation is normalised bythe prompt (P) correlation value. In a GPS receiver usingearly-minus-late code phase tracking, the code phase tracking error (Δt)can therefore be approximated whereby: $\begin{matrix}{{\Delta \quad t} = {\frac{1}{g}\Delta \quad \left\{ \frac{E - {L \pm n_{e}} + n_{l}}{P \pm n_{p}} \right\}}} & \text{[Equation~~2]}\end{matrix}$

[0037] where g is the gradient of the (E−L)/P graph at t=0; E, L and Pare correlation measurements; and n_(e), n_(I) and n_(p) are early, lateand prompt correlation measurement noise respectively.

[0038] Assuming the noise to be small and uncorrelated, at E−L=0, thecode phase error Δt can be expressed as follows: $\begin{matrix}{{\Delta \quad t} \approx {\frac{1}{g}\quad \frac{\sqrt{2}n}{P}}} & \text{[Equation~~3]}\end{matrix}$

[0039] where n is the magnitude of the effective noise.

[0040] It is therefore possible to define a figure of merit (FOM) whichis approximately directly proportional to the receiver accuracy:$\begin{matrix}{\left( {{{FOM} = \frac{\left( {E - L} \right)}{t}}} \right)_{t = 0} \times n} & \text{[Equation~~4]}\end{matrix}$

[0041] A finite length pseudorandom noise code may be approximated to anideal random binary code. Accordingly, there is no periodicity of thecorrelation and therefore no line quantisation of the correlation powerspectrum.

[0042] The power spectrum of the correlation is given by the Fouriertransform of the correlation power. Since there is no Fourier transformof a truly random binary code, in order to obtain the power spectrum,the Fourier transform of the autocorrelation function is calculated. Fora binary code having an amplitude of ±A, the autocorrelation function isthe classic triangular shape with a base length of ±1 code chip and amaximum correlation power of A². This can be expressed as follows:$\begin{matrix}{{{R(\tau)} = {{{A^{2}\left( {1 - \frac{\tau }{T_{c}}} \right)}\quad {for}\quad {\tau }} \leq T_{c}}}{{R(\tau)} = {{0\quad {for}\quad {\tau }} > T_{c}}}} & \text{[Equation~~5]}\end{matrix}$

[0043] where T_(c) is the chip period for the C/A code). The Fouriertransform of this is given by. $\begin{matrix}{{S(\omega)} = {A^{2}T_{c}\sin \quad c^{2}\omega \quad \frac{Tc}{2}}} & \text{[Equation~~6]}\end{matrix}$

[0044] As the correlation power can be derived from the inverse Fouriertransform of the correlation power spectrum, it is therefore possible touse the power spectrum as a starting point for the derivation of thecorrelation function shape and size. Also, the power spectrum can bemodified to reflect the consequences of any front-end filtercharacteristics and the Fourier transform taken of the resultingspectrum to derive the correlation characteristics. Although this doesnot take account of several significant effects, such as the lowresolution ADC in an actual system, the qualitative results appear to beconsistent with theorised models.

[0045] To do this, an idealised power spectrum is first generated over arange of frequencies (say ±8MHz or ±12MHz in 0.02MHz steps) and held ina vector. The vector can then be “filtered” by multiplying individualelements by a transmission factor. The simplest form of filtering onlyuses filter transmissions of zero or one. The power spectrum isnormalised to an amplitude, A, of unity.

[0046] The precise correlation can then be generated from the powerspectrum by taking the inverse Fourier transform. This is a vectorcontaining the correlation as a function of time, expressed in terms ofthe chip period T_(c). The total length of the vector (i.e. the range oftime) is inversely proportional to the frequency step size of the powerspectrum and the correlation step size is inversely proportional to thetotal range of the power spectrum.

[0047] The early-minus-late correlation can be generated by a sparsematrix operation on the precise correlation vector.

EL(t)=M _((E−L)) .P(t)

[0048] where EL(t) is a column vector containing the (E−L) correlationresult, P(t) is a column vector containing the precise correlationresult and M_((E−L)) is a square matrix whose dimension is the same asthe vector lengths. The matrix M_((E−L)) is mainly zero but containselements of ±1 on diagonals which perform the (E−L) arithmeticoperation. An example is shown below: $\begin{matrix}{M_{({E - L})} = \begin{pmatrix}0 & 0 & 1 & 0 & 0 & 0 & \cdots & 0 \\0 & 0 & 0 & 1 & 0 & 0 & \cdots & 0 \\{- 1} & 0 & 0 & 0 & 1 & 0 & \cdots & 0 \\0 & {- 1} & 0 & 0 & 0 & 1 & \cdots & 0 \\0 & 0 & {- 1} & 0 & 0 & 0 & \cdots & 1 \\0 & 0 & 0 & {- 1} & 0 & 0 & \cdots & 0 \\\vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \quad & \vdots \\0 & 0 & 0 & 0 & {- 1} & 0 & \cdots & 0\end{pmatrix}} & \text{[Equation 7]}\end{matrix}$

[0049] The distance of the leading element of each diagonal from thetop-left corner of the matrix gives the early-minus-late spacing andwill depend on the time resolution of the correlation vector.

[0050] In FIG. 4, curve 41 shows the FOM, i.e. the gradient of theearly-minus-late correlation function, varying with the half-bandwidthof incoming signal. This is due to the shape of the correlation peakbeing modified by the varying sum of its Fourier components. The reasonfor the variation in FOM with bandwidth is further explained by thepower spectrum of the correlation described by curve 51 in FIG. 5A. Thepower spectrum has nulls at 1, 2 , . . . n MHz. Between 0 and 1 MHz,even Fourier components contribute to the power, between 1 and 2 MHz oddFourier components contribute to the power (etc.). These even and oddcomponents eventually mix to form the ideal triangular correlationshape. However, even components serve to increase the steepness of thecorrelation shape around t=Tc/2 while odd components serve to decreasethe steepness. For half-chip (E−L) correlators, an increase in thesteepness of the correlation shape at Tc/2 results in an increased (E−L)gradient at t-0 and therefore an improved FOM.

[0051] The idea behind this invention is to selectively allow the evencomponents of the signals to contribute to the correlation whileblocking the odd components. In practice, to limit the requiredbandwidth, only the first few components would be used. The resultingmodified power spectrum is described by curve 52 in FIG. 5B, suggestingthat the FOM can be increased by about 14% in this way.

[0052] Even greater increases in the FOM can be achieved by artificiallyadapting the shape of the correlation. Curve 53 of FIG. 5B described thesituation where the odd components have been removed and the firstharmonic even components increased by a factor of 2. The FOM is nowincreased by a factor of about 28%. Thus, this invention provides amethod of increasing the accuracy of a GPS system which uses codetracking only.

[0053] As previously stated, in a GPS receiver of the type shownschematically in FIGS. 1 and 2, the preprocessing, receiver channel andreceiver processor will typically be implemented in the form of frontend analogue circuitry combined with either a general purposemicroprocessor or a microprocessor embedded in a GPS applicationspecific integrated circuit. Implementation of a method of code phasetracking according to the present invention, including the example asdescribed below, may be accomplished by appropriate analogue circuitrydesign and/or microprocessor programming. Of course, such design andprogramming is well known and would be accomplished by one of ordinaryskill in the art of GPS and CDMA communication without undue burden.

1. A method of code phase tracking comprising the steps of: (a)receiving a subject signal containing a target pseudorandom noise code;(b) generating a series of signals containing early and late replicacodes corresponding to the target code; (c) correlating the subjectsignal with the early and late replica code signals and returningrespective early and late correlation values; and (d) determining thecode phase error between the target code and the replica codes from amodified early-minus-late correlation function derived from the earlyand late correlation values, the modified early-minus-late correlationfunction being such that its gradient at zero code phase error isincreased compared to the true early-minus-late correlation function. 2.A method according to claim 1 wherein the early-minus-late correlationfunction is modified by modifying either the subject signal, the earlyand late replica code signals or the early and late correlation valuesprior to deriving the early-minus-late correlation function.
 3. A methodaccording to claim 2 wherein at least one odd harmonic of the powerspectrum of the subject signal is reduced in size or removed.
 4. Amethod according to claim 2 wherein at least one even harmonic of thepower spectrum of the subject signal is increased in size.
 5. A methodaccording to claim 2 wherein the bandwidth of the power spectrum of thesubject signal is truncated between harmonics so as to excise anadjacent even harmonic.
 6. A method according to claim 2 wherein atleast one odd harmonic of the power spectrum at least one of the earlyand late replica code signals is reduced in size or removed.
 7. A methodaccording to claim 2 wherein at least one even harmonic of the powerspectrum at least one of the early and late replica code signals isincreased in size.
 8. A method according to claim 2 wherein thebandwidth of the power spectrum at least one of the early and latereplica code signals is truncated between harmonics so as to excise anadjacent even harmonic.
 9. A method of code phase tracking substantiallyas hereinbefore described with reference to the figures.
 10. A receivercomprising an antenna for receiving a subject signal containing a targetpseudorandom noise code; and a signal processor for implementing amethod of code phase correlation according to any preceding claim.
 11. Areceiver comprising a signal processor for modifying the power spectrumof a received subject signal containing a target pseudorandom noise codeso that the power spectrum of the subject signal has either at least oneodd harmonic which is reduced in size or removed; at least one evenharmonic which is increased in size; or a reduced bandwidth which istruncated between harmonics so as to excise an adjacent even harmonic.12. A receiver comprising an antenna for receiving a subject signalcontaining a target pseudorandom noise code and a signal processor, thesignal processor comprising a generator for generating a series ofsignals containing early and late replica codes corresponding to thetarget code, a correlator for correlating the subject signal with theearly and late replica code signals and returning respective early andlate correlation values, and means for determining the code phase errorbetween the target code and the replica codes from a modifiedearly-minus-late correlation function derived from the early and latecorrelation values, such that the gradient of the modifiedearly-minus-late correlation function at zero code phase error isincreased compared to the true early-minus-late correlation function.13. A receiver according to claim 12 wherein the early-minus-latecorrelation function is modified by modifying either the subject signal,the early and late replica code signals or the early and latecorrelation values prior to deriving the early-minus-late correlationfunction.
 14. A receiver according to claim 13 wherein at least one oddharmonic of the power spectrum of the subject signal is reduced in sizeor removed.
 15. A receiver according to claim 13 wherein at least oneeven harmonic of the power spectrum of the subject signal is increasedin size.
 16. A receiver according to claim 13 wherein the bandwidth ofthe power spectrum of the subject signal is truncated between harmonicsso as to excise an adjacent even harmonic.
 17. A receiver according toclaim 13 wherein at least one odd harmonic of the power spectrum atleast one of the early and late replica code signals is reduced in sizeor removed.
 18. A receiver according to claim 13 wherein at least oneeven harmonic of the power spectrum at least one of the early and latereplica code signals is increased in size.
 19. A receiver according toclaim 13 wherein the bandwidth of the power spectrum at least one of theearly and late replica code signals is truncated between harmonics so asto excise an adjacent even harmonic.
 20. A receiver substantially ashereinbefore described with reference to the figures.